# Rotational inertia of a wheel

1. Nov 2, 2007

### Mr. Sinister

1. The problem statement, all variables and given/known data
A force of 21.09 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s ^2. Calculate the rotational inertia of the wheel.

a) 7.46 kg . m2
b) 4.98 kg . m2
c) 8.96 kg . m2
d) 5.97 kg . m2

2. Relevant equations

Do I use some type of inertia equation?

3. The attempt at a solution

My problem is I seem to not know where to start?

2. Nov 2, 2007

### hage567

The force is creating a torque on the disk. Can you relate torque to force, and torque to angular acceleration? There are two equations you need to use and put together to find the moment of inertia.

3. Nov 2, 2007

### Mr. Sinister

I found an equation that states the total torque equals the moment of inertia of the body. Does this help me somehow?

4. Nov 2, 2007

### hage567

Well I think you're missing a bit. Does that equation look like this

$$\tau=I\alpha$$ where $$\alpha$$ is angular acceleration.

Yes, you need this.

Now you need to find a way to relate torque to force.

5. Nov 2, 2007

### Mr. Sinister

Ok, cool, I found radius times force times sin theta which equals torque.

6. Nov 2, 2007

### Mr. Sinister

It seems I have the radius and force for the equation but I don't have Sin. Is the wheel considered 360 degrees?

7. Nov 2, 2007

### hage567

You don't have to consider the angle here because the force is applied tangentially to the rim of the wheel (so sin90 = 1), and not at an angle.

8. Nov 2, 2007

### Mr. Sinister

Ok, so for Torque I have 7.17. In the equation that you gave me I do not have inertia but I do have angular acceleration. How do solve for inertia and tie these two ends together?

9. Nov 2, 2007

### hage567

In the equation I gave you in post #4, I is the moment of inertia. You know what the torque is now, so you can find I.

10. Nov 2, 2007

### Mr. Sinister

Great, Thank You very much ! You are extremely helpful! I know you helped me last time too. I wish I could figure out how to tackle these problems from the get go. How do I know which equations to use?

11. Nov 2, 2007

### hage567

Well, you need to know the physical concepts so you know what's going on in the problem and can pick the right course of action. Knowing what the equations mean is also important. Drawing a diagram and listing everything you know and everything you need helps to keep track of things. Other than that, just practice. The more problems you do the easier it becomes for you to see how to solve them.

12. Nov 2, 2007

### Mr. Sinister

Nice, thanks. I have a test next week and I am trying to figure out some of these problems. I will probably post another one here.